On the way to fullerenes : molecular dynamics study of the Curling and closure of graphitic ribbons

Sparked by the synthetic breakthrough of Kratschmer, Huffman, and co-workers yielding macroscopic amounts of research on the fullerenes (discovered 5 years earlier3) has continued to accelerate. Despite the pace of this research, the mechanisms leading to the facile formation of highly symmetric fullerene cages in the chaotic conditions of the carbon arc remain to be ~larified."~ In this Letter, following ideas advanced by Smalley, Curl, Kroto, and co-workers,eE we use molecular dynamics (MD) simulations to study the behavior of graphitic fragments thought to condense in the cooling carbon vapor prior to fullerene formation. These fragments are treated as ribbons as an idealization of their probable low-symmetry, far-from-circular shapes. At the conditions present in the carbon arc, we find that such ribbons can exhibit large thermal fluctuations from planarity without fragmentation. These fluctuations, when sup plemented by the curvature induced by pentagons, often cause these isolated strips spontaneously to form open-ended hollow carbon structures. Once formed, these hollow structures represent good fullerene precursors. Graphitic ribbons are modeled using a bond-order type empirical hydrocarbon potentiallo which accurately predicts the bonding and energetics of solid diamond lattices and graphite sheets, as well as hydrocarbon molecules, while still allowing reactions to occur. The reactive aspect of the potential is important both to model correctly the reactive edges of these ribbons and to allow for any possible fragmentation at high temperature. Although this potential has already been shown to provide a good model for a wide variety of properties of fullerenes and related structure~,~~-~~ to assess further its reliability for the present study we examined the energetics of the inversion of the corranulene molecule (Cal0). This molecule is similar in shape to one-third of a buckminsterfullerene cluster. Recent studies have shown that corranulene can rapidly fluctuate between two curved minima at room temperature14-a behavior that is related to the ribbon motions discussed below. First principles calculations yield an energy difference between the minimum-energy curved structures and a planar intermediate of 8.8-1 1.0 kcal/mol.l5J6 Our empirical potential predicts a difference of 10.3 kcal/mol, in excellent agreement with these calculations.